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Does it Pay to Have Fat Tails? Examining Kurtosis and the Cross-Section of Stock Returns

Xiong and Idzorek (2011) show that extremely large price movements, which are rare under a normal distribution, occur approximately 10 times more often than predicted by a normal distribution indicating that the normality assumption required in many asset pricing models is often violated. When examining whether the higher moments of return distributions are priced in stocks, prior research has demonstrated that skewness predicts negative returns. While some studies have investigated the return premium associated with skewness, fewer studies have focused on the relation between kurtosis and future returns. In this paper we attempt to determine whether there is a significant return premium associated with kurtosis. Using a broad sample of stocks 1980 to 2010, we find that the average stock exhibits excess kurtosis and that kurtosis is negatively related to firm size and positively related to volatility and turnover. Further, we show that stocks with high kurtosis have higher raw returns than stocks with low kurtosis. However, when we control for other risk factors that are more common in traditional asset pricing models, the return premium associated with kurtosis vanishes. These results indicate that kurtosis is not priced in stocks.